The Elusive Costs of Inflation: Price Dispersion During the U.S. Great Inflation

Introduction

• A central question for central banks is determining the optimal inflation rate target.
• This decision hinges on understanding the costs associated with inflation.
• A significant concern is that high inflation may lead to inefficient price dispersion, distorting the allocative role of the price system.
• New Keynesian models suggest that the cost of inflation is substantial. Moving from 0% to 10% inflation could result in a welfare loss greater than those caused by business cycle fluctuations.
• The study empirically assesses this prediction using price data from the Great Inflation period (late 1970s and early 1980s) in the U.S.
• The study aims to determine if the absolute size of price changes increased with inflation, which would indicate prices drifting further from their optimal levels at higher inflation rates.
• The study found no evidence indicating that the absolute size of price changes rose during the Great Inflation.
• This suggests the standard New Keynesian analysis of inflation's welfare costs might be incorrect, requiring a reassessment of optimal inflation rate implications.
• The research also indicates that (non-sale) prices haven't become more flexible over the past 40 years.

Reconsideration of Optimal Inflation Levels

• Before the Great Recession, there was a consensus among policymakers to target inflation rates close to zero, with some countries adopting explicit targets around 2% per year.
• Some academic studies even argued for lower inflation rates, considering the zero lower bound (ZLB) on nominal interest rates.
• The Great Recession has prompted a reevaluation, with some economists advocating for higher inflation targets, such as 4% per year.
• A concern with higher inflation is the increased price dispersion, which could distort the price system's allocative role.
• In a high-inflation environment, relative prices may fluctuate inefficiently as prices drift from their optimal values between adjustments.
• This could lead to incorrect signals regarding relative production costs, compromising production efficiency.
• Standard New Keynesian models suggest these costs are substantial even at moderate inflation levels.
• Calibrated models show that moving from 0% to 12% inflation could lead to a consumption-equivalent welfare loss of about 10%.
• This loss is far greater than the welfare costs of business cycle fluctuations, which supports the idea of virtual price stability in these models.

Challenges in Measuring Price Dispersion Sensitivity

• One challenge is the limited variation in the inflation rate in the U.S. over the past few decades.
• BLS micro-data has been influential in establishing facts about price changes, but it primarily covers the post-1987 period when inflation was low and stable.
• To address this, researchers extended the BLS micro-data back to 1977 in order to analyze a period of sharply rising inflation, which peaked around 12% in 1980, followed by a dramatic decrease led by the Federal Reserve under Paul Volcker (see Figure I).
• The new data was constructed from original microfilm cartridges at the BLS, which were scanned and converted using custom OCR software.
• The process took several years because the data was restricted to the BLS building in Washington, DC.
• Another challenge is the presence of unobserved product heterogeneity.
• Much of the cross-sectional dispersion in prices, even within narrow product categories, likely results from differences in product size and quality.
• Calculating the standard deviation of prices within a category will lump together desired price dispersion from product heterogeneity and inefficient price dispersion from price rigidity.
• Desired price dispersion within even narrow categories is likely to overshadow inefficient price dispersion at moderate inflation levels.
• The existing literature has argued that desired real prices of a product vary significantly over time (Golosov and Lucas 2007).
• This indicates that simple reduced-form approaches to "differencing out" product heterogeneity, such as analyzing deviations from a product’s mean real level, may not be effective.

Earlier Research and Methodological Shift

• Earlier studies of the relationship between price dispersion and inflation faced similar challenges (Van Hoomissen 1988; Lach and Tsiddon 1992).
• These studies concluded that directly studying price dispersion was not viable and instead focused on price change dispersion.
• The researchers argued that price change dispersion is an acceptable proxy for price dispersion in menu cost models.
• However, this is not true even qualitatively in more empirically realistic menu cost models used today.
• In these models, price change dispersion actually falls with inflation at low levels, while price dispersion remains roughly flat.
• At low inflation rates, a significant fraction of price changes are decreases, leading to a dispersed distribution of price changes.
• As inflation increases, the frequency of price decreases falls, narrowing the price change distribution to include mostly increases, reducing the cross-sectional variance of price changes.

Current Approach: Absolute Size of Price Changes

• To overcome the challenge, this study assesses the sensitivity of inefficient price dispersion to inflation changes by examining how the absolute size of price changes varies with inflation.
• If inflation leads prices to deviate further from their optimal level, adjustments should be larger.
• If inefficient price dispersion rose during the Great Inflation, the absolute size of price changes should have risen as well.
• This intuition is tested in the Calvo model and in a Golosov-Lucas style menu cost model (with large idiosyncratic shocks of prices needed to explain the large frequency and size of price changes at low levels of inflation).
• In the Calvo model, the average absolute size of price changes rises rapidly with inflation, as does inefficient price dispersion.
• In the menu cost model, the average absolute size of price changes and inefficient price dispersion are virtually flat over inflation rates relevant to the study.
• Firms find it optimal to pay the relatively small menu cost before prices drift too far, limiting the extent to which price dispersion rises with inflation, reducing the welfare loss from increasing inflation when there are large idiosyncratic shocks (Burstein and Hellwig, 2008).
• The mean absolute size of price changes in the U.S. is essentially flat over the sample period.
• Additionally, the standard deviation of the absolute size of price changes is also essentially flat.
• There is no evidence that prices deviated more from their optimal level during the Great Inflation (when inflation was running at consistently higher than 10% a year) than during the more recent period (when inflation has been closer to 2% a year).
• Because of this, the research concludes that the main costs of inflation in the New Keynesian model are completely elusive in the data.
• This implies that conclusions about the optimality of low inflation rates, reached by researchers using models of this kind, need to be reassessed.

Frequency of Price Change and Model Comparison

• Rather than an increase in the absolute size of price changes during the Great Inflation, there was instead a substantial increase in the frequency of price change.
• The behavior of both the absolute size and frequency of price change as inflation varies in the sample align much better with the predictions of menu cost models than with the predictions of the Calvo model.
• In this regard, the results reinforce results based on micro-data from several other countries (e.g., Gagnon 2009; Alvarez et al. 2016).

Price Flexibility and Technological Change

• Despite technological changes over the last four decades, regular prices (excluding temporary sales) do not seem to have become more flexible, controlling for inflation.
• A simple menu cost model with a fixed menu cost over the entire sample can match the empirical relationship between the frequency of price change and inflation.
• Menu costs represent deeper frictions in the price adjustment process arising from technological, managerial, or customer-related factors.
• These costs do not appear to be going away over time.
• In sharp contrast, the frequency of temporary sales has increased substantially over the past four decades.
• Temporary sales occur only in a subset of sectors, but their frequency has increased substantially in all of these sectors.
• Whether this has important implications for aggregate price flexibility has been a topic of active research over the past decade.
• The empirical literature has emphasized that temporary sales have quite different empirical properties from those of regular prices; sales are much more transitory than other price changes and less responsive to macroeconomic conditions.
• These characteristics substantially limit the contribution of temporary sales to aggregate price flexibility (Arguments made in Nakamura and Steinsson (2008), Guimaraes and Sheedy (2011), Kehoe and Midrigan (2015), and Anderson et al. (2015).).
• Moreover, this growth in temporary sales leaves the large and growing “gorilla in the room” sector—the service sector—untouched.

Previous Studies on Price Dispersion and Inflation

• Relatively little work has been done on the sensitivity of price dispersion to changes in inflation in the United States.
• Reinsdorf (1994) used BLS microdata for the period 1980–1982 (a subset of the study's data) and found that price dispersion rose when inflation fell.
• Sheremirov (2015) used scanner price data for the relatively low inflation period of 2002–2012 and found that price dispersion rises with inflation.
• Alvarez et al. (2016) studied the relationship between price dispersion and inflation during the Argentinian hyperinflation in 1989–1990 and found that the elasticity of price dispersion with inflation is roughly one-third at high inflation rates, in line with a simple menu cost model.
• The stability of the absolute size of price changes at different levels of inflation that the study finds in the data is consistent with earlier work.
• Cecchetti (1986) analyzed magazine prices at newsstands and found that the absolute size of price changes is stable over his sample period of 1953 to 1979.
• Gagnon (2009) found that the absolute size of price changes varies little with inflation in Mexico during a large bout of inflation in the mid-1990s.
• Wulfsberg (2016) similarly found that the absolute size of price changes varies very little in Norway over the Great Inflation period.
• Using scraped data from the internet, Cavallo (2015) found that the absolute size of price changes does not vary much across countries with very different levels of inflation.

Model Setup

• The model economy consists of households, firms, and a government.
• The households maximize discounted expected utility: $Et \sum<em>{j=0}^{\infty} \beta^j [\log C</em>{t+j} - L_{t+j}]$ Where:
  • $E_t$ is the expectations operator.
  • $C_t$ is household consumption of a composite good.
  • $L_t$ is household labor supply.
  • $\beta$ is the discount factor.
• The composite consumption good is an index of individual goods: $C<em>t = (\int</em>{0}^{1} c_{it}^{\frac{\theta-1}{\theta}} di)^{\frac{\theta}{\theta-1}}$ Where:
  • $c_{it}$ is consumption of individual product i.
  • \theta > 1 is the elasticity of substitution between products.
• The household's budget constraint is: $P<em>t C</em>t + Q<em>{it} B</em>{it} = W<em>t L</em>t + (D<em>{it} + Q</em>{it}) B_{it-1}$ Where:
  • $P_t$ is the aggregate price index.
  • $Q_{it}$ is the price of asset i.
  • $B_{it}$ is the quantity of asset i.
  • $W_t$ is the wage rate.
  • $D_{it}$ is the dividend from firm i.
• Households minimize the cost of attaining a consumption level $C<em>t$, which implies demand for individual product i: $c</em>{it} = (\frac{p<em>{it}}{P</em>t})^{-\theta} C_t$
• The aggregate price index is defined as:
  $P<em>t = (\int</em>{0}^{1} p_{it}^{1-\theta} di)^{\frac{1}{1-\theta}}$
• Optimal labor supply is given by:
  $\frac{W<em>t}{P</em>t} = C_t$
• The household's valuation at time t of an uncertain dividend payment from firm i at time t + j is:
  $V<em>{it}^j = E</em>t [\beta^j (\frac{C<em>{t+j}}{C</em>t})^{-1} D_{i,t+j}]$

Firm Behavior

• Firms produce distinct individual products using the production function: $y<em>{it} = A</em>{it} L_{it}$ Where:
  • $A_{it}$ is the productivity level of firm i.
  • $L_{it}$ is the amount of labor demanded by firm i.
• Firm productivity varies over time according to the AR(1) process: $\log A<em>{it} = \rho \log A</em>{i,t-1} + \epsilon_{it}$ Where:
  • $\epsilon<em>{it} \sim N(0, \sigma</em>{\epsilon}^2)$ are independent over time and across firms.
• Firms meet demand at posted prices and hire labor at wage rate $W_t$ to satisfy demand.
• The marginal cost of firm i is:
  $MC<em>{it} = \frac{W</em>t}{A_{it}}$
• Firms are monopoly suppliers and their main decision is how to price products, considering price-changing costs.
• The monetary authority controls nominal output: $\log S<em>t = \mu + \log S</em>{t-1} + \eta_t$ Where:
  • $S<em>t = P</em>t C_t$ is nominal output.
  • $\eta<em>t \sim N(0, \sigma</em>{\eta}^2)$ are independent over time.

Flexible Price Benchmark

• With flexible prices, firms set prices as a markup over marginal cost:
  $p<em>{it} = \frac{\theta}{\theta - 1} \frac{W</em>t}{A_{it}}$
• At the aggregate level, the price level is:
  $P<em>t = \frac{\theta}{\theta - 1} \frac{W</em>t}{A<em>f}$ Where $A</em>f = (\int<em>{0}^{1} A</em>{it}^{\theta-1} di)^{\frac{1}{\theta-1}}$
• Aggregate production function:
  $Y<em>t = A</em>f L_t$
• Equilibrium values of output, labor, and real wages are determined by:
  • Labor supply: $\frac{W<em>t}{P</em>t} = Y_t$
  • Production function: $Y<em>t = A</em>f L_t$
  • Markup: $P<em>t = \mu</em>f \frac{W<em>t}{A</em>f}$, where $\mu_f = \frac{\theta}{\theta-1}$
• Nominal prices and wages are determined by adding $S<em>t = P</em>t Y_t$ to the system.
• Output and labor supply are independent of the inflation rate and shocks to nominal aggregate demand.
• The only distortion is the monopoly power of firms, leading to prices above marginal costs and inefficiently low output.

Equilibrium with Sticky Prices

• Equilibrium determination is more complex and depends on price adjustment costs (constant fixed cost/menu cost model, or Calvo 1983 model).
• Firms maximize the value of their stochastic stream of dividends.

Analogous Equations for Sticky Price Equilibrium

• Equations analogous to the flexible price model, but with sticky prices:
  • Labor supply: $\frac{W<em>t}{P</em>t} = Y_t$
  • Production function: $Y<em>t = A</em>t(\bar{\pi})(L<em>t - L</em>{pc,t})$
  • Price setting: $P<em>t = \mu</em>t(\bar{\pi}) \frac{W<em>t}{A</em>t(\bar{\pi})}$ Where:
    • $\bar{\pi}$ denotes the average inflation rate.
    • $L_{pc,t}$ denotes extra labor needed to change prices.
• Aggregate labor productivity with sticky prices:
  $A<em>t(\bar{\pi}) = (\int</em>{0}^{1} (\frac{p<em>{it}}{P</em>t})^{-\theta} A_{it}^{-1} di)^{-1}$
• Aggregate markup in the sticky-price case: $\mu_t(\bar{\pi})$
• Output and labor supply under sticky prices differ from flexible prices due to:
  • Lower aggregate labor productivity.
  • Differences in the aggregate markup.
• Welfare depends on output and labor, measured by consumption-equivalent welfare changes:
  $E[\log(\lambda(1 + \Lambda)C<em>t^A) - L</em>t^A] = E[\log(C<em>t^B) - L</em>t^B]$

Model Calibration

• Models calibrated for menu cost and Calvo models (both with idiosyncratic productivity shocks).
• Time unit corresponds to a month.
• Subjective discount factor: $\beta = 0.96^{\frac{1}{12}}$.
• Elasticity of substitution: $\theta = 4$ (and $\theta = 7$ for comparison).
• Menu cost model: Menu cost (K) and standard deviation of idiosyncratic shocks $\sigma<em>{\epsilon}$ calibrated to match median frequency of price change (10.1% per month) and median absolute size of price changes (7.5%) over the period 1988–2014, resulting in $K = 0.019$ and $\sigma</em>{\epsilon} = 0.037$.
• Calvo model: Frequency of price change set equal to the median frequency in the data, and standard deviation of idiosyncratic shocks equal to the menu cost model ($\sigma_{\epsilon} = 0.037$).
• First-order autoregressive parameter for idiosyncratic productivity: $\rho = 0.7$.
• Standard deviation of shocks to nominal aggregate demand: $\sigma_{\eta} = 0.0039$.

Numerical Results on the Costs of Inflation

• Figure II plots the consumption-equivalent welfare loss experienced by households when prices are sticky relative to welfare when prices are completely flexible, as a function of the inflation rate.

• The difference in results between the menu cost model and the Calvo model is striking.

• For the menu cost model, the welfare loss is small and virtually completely constant at about 0.4% as a function of inflation; this is true both when $\theta = 4$ and $\theta = 7$.

• For the Calvo model, the costs of price rigidity rise sharply with inflation.

  Data Set Construction

• The BLS CPI Research Database formerly contained data starting in 1988, which did not cover the Great Inflation.

• The construction of the data set involved two main phases:

  • Scanning the physical microfilm cartridges to convert them to digital images.
  • Converting the images of Price Trend Listings to machine-readable form, which involved custom OCR software.

Data Characteristics

• The data set spans from May 1977 to October 1986, and May to December 1987.
• Each Price Trend Listing contains prices for the previous 12 months for a given product.
• The data includes the following information:
  • Entry Level Item (ELI)
  • Location (city) identifier
  • Outlet identifier
  • Product identifier
  • Product's price
  • Percentage change in the product's price between collection periods
  • "Sales flag"
  • "Imputation flag"
  • Additional flags that are not used in this study

Data Validation

• The raw data contains redundancies that allow for error checking in the OCR procedure:
  • Prices appear on multiple Price Trend Listings since the listings include 12 months of previous prices.
  • Each Price Trend Listing includes both the price and the percentage change variable.

Price Dispersion and Product Heterogeneity

• Figure VI plots the evolution of a simple measure of price dispersion for U.S. consumer prices over the period 1978–2014.
• The figure shows that this simple measure of price dispersion has increased steadily over the past 40 years.
• As discussed, a key empirical challenge is that much of the cross-sectional dispersion in prices results from heterogeneity in product size and quality.

Fixed-Effects Price Gap

• The statistic $x<em>{ijt} = log p</em>{ijt} − log P<em>{jt} − \frac{\sum</em>{τ=t<em>{ij}^0}^{T</em>{ij}} [log p<em>{ijτ} − log P</em>{jτ}]}{T<em>{ij} − t</em>{ij}^0 + 1}$, referred to as the "fixed-effects price gap," measures the real price of product $ij$ relative to its mean over the entire period for which a price is observed for this product.

Absolute Size of Price Changes

• The study proposes to focus on the times when prices change to overcome difficulties in measuring price dispersion directly.
• At these times, a substantial amount of information is revealed about the product’s desired price and the distance a product’s price has drifted from its desired price.
• The study argues that if higher inflation truly leads prices to drift further from their efficient levels, we should observe larger price changes when firms finally adjust their prices.
• This suggests that the absolute size of price changes may be a good proxy for inefficient price dispersion.

Frequency of Price Change

• The frequency of price change is in some sense the flip side of the coin.
• If inflation rises but the size of price changes doesn’t, the frequency of price change must be changing.
• Figure XIV plots the frequency of price change for consumer prices in the United States over the sample period of 1978–2014 along with the CPI inflation rate.
• The figure clearly shows that the frequency of price change comoves strongly with inflation.
• Figure XV separates the frequency of price increases and the frequency of price decreases.
• The most striking feature of this figure is that it is the frequency of price increases that varies with the inflation rate, while the frequency of price decreases is unresponsive.

Have Prices Become More Flexible Over Four Decades?

• There is no evidence that prices (excluding sales) have become more flexible over time.
• One measure of price flexibility is the menu cost needed to match the frequency of price change at a particular point in time given the level of inflation at that time.
• Figure XVI presents the results of this type of exercise.
• Figure XVII plots the evolution of the frequency of sales in the sectors in which sales are prevalent.

Conclusion

• The study develops a new comprehensive micro-price dataset going back four decades for U.S. consumer prices to study the costs of inflation.
• There is little evidence that the Great Inflation led to a substantial increase in price dispersion.
• The frequency of price change varies substantially with the inflation rate, which is consistent with the predictions of standard menu cost models.
• There is no evidence that regular prices have become more flexible over these four decades, suggesting that the barriers to price adjustment are not technological in nature.